Integral Calculus: Basic Integration of cotxln(sinx)

[whatlifeforme]

Homework Statement

evaluate the integral.

Homework Equations

$\int (cotx)[ln(sinx)] dx$

how would i do this using basic integration techniques from calculus 1? i am not allowed to use, int by parts, partial fractions, trig sub, etc..

The Attempt at a Solution

i tried doing a u=sinx but don't know how to get the cotx.

 

[SammyS]

Homework Statement

evaluate the integral.

Homework Equations

$\int (cotx)[ln(sinx)]$

how would i do this using basic integration techniques from calculus 1? i am not allowed to use, int by parts, partial fractions, trig sub, etc..

The Attempt at a Solution

i tried doing a u=sinx but don't know how to get the cotx.

Where's the "dx" ?

$\displaystyle \int \cot(x)\ln(\sin(x))\,dx$

This may help. $\displaystyle \ \cot(x)=\frac{\cos(x)}{\sin(x)}$

 

[whatlifeforme]

thanks.

so i have:

u=sinx; du=cosx

$\int \frac{ln(u)}{u} du$

v=lnu; dv=(1/u) du

$\int v dv$ = $\frac{v^2}{2}$ = $\frac{(lnu)^2}{2}$

= $\frac{[ln(sinx)]^2}{2}$

 

[iRaid]

thanks.

so i have:

u=sinx; du=cosx

$\int \frac{ln(u)}{u} du$

v=lnu; dv=(1/u) du

$\int v dv$ = $\frac{v^2}{2}$ = $\frac{(lnu)^2}{2}$

= $\frac{[ln(sinx)]^2}{2}$

Looks good to me, other than the +C.